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Some C*-Algebras with Outer Derivations, II

Published online by Cambridge University Press:  20 November 2018

George A. Elliott
George A. Elliott*
Affiliation:
The Institute for Advanced Study, Princeton, New Jersey
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In this paper we shall consider the class of C*-algebras which are inductive limits of sequences of finite-dimensional C*-algebras. We shall give a complete description of those C*-algebras in this class every derivation of which is inner.

Theorem. Let A be a C*-algebra. Suppose that A is the inductive limit of a sequence of finite-dimensional C*-algebras. Then the following statements are equivalent:

(i) every derivation of A is inner;

(ii) A is the direct sum of a finite number of algebras each of which is either commutative, the tensor product of a finite-dimensional and a commutative with unit, or simple with unit.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 185 - 189
Copyright
Copyright © Canadian Mathematical Society 1974

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